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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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An alternative to complete topological vector spaces in the framework of condensed mathematics.
Roughly, completeness is expressed as ability to integrate with respect to Radon measures.
This doesn’t quite work as stated, and to make this rigorous one has to bring L^p-spaces for 0<p≤1 (i.e., the non-convex case) into the picture.
A condensed abelian group V is p-liquid (0<p≤1) if for every compact Hausdorff topological space S and every morphism of condensed sets f:S→V there is a unique morphism of condensed abelian groups MUnknown characterp(S)→V that extends f along the inclusion S→MUnknown characterp(S).
Here for a compact Hausdorff topological space S and for any p such that 0Unknown characterp≤1 we have
MUnknown characterp(S)=⋃qUnknown characterpMq(S),where
Mp(S)=⋃CUnknown character0M(S)ℓp≤C,where
M(S)ℓp≤C=limiM(Si)ℓp≤C,where Si are finite sets such that
S=limiSiand
M(F)ℓp≤Cfor a finite set F denotes the subset of RF consisting of sequence with l^p-norm at most C.
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